Chapter 2

For the following exercises, graph the pair of equations on the same axes, and state whether they are parallel, perpendicular, or neither. \(3 x-2 y=5\) \(6 y-9 x=6\)

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ \frac{2+\sqrt{-12}}{2} $$

Determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve. $$ 6 x^{2}-x-2=0 $$

For each of the following exercises, construct a table and graph the equation by plotting at least three points. $$2 y=x+3$$

For the following exercises, solve the equation by identifying the quadratic form. Use a substitute variable and find all real solutions by factoring. $$ 4(t-1)^{2}-9(t-1)=-2 $$

For the following exercises, graph the pair of equations on the same axes, and state whether they are parallel, perpendicular, or neither. \(y=\frac{3 x+1}{4}\) \(y=3 x+2\)

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ \frac{4+\sqrt{-20}}{2} $$

The area of a trapezoid is given by \(A=\frac{1}{2} h\left(b_{1}+b_{2}\right)\) Use the formula to find the area of a trapezoid with \(h=6, b_{1}=14,\) and \(b_{2}=8\)

Solve the quadratic equation by using the quadratic formula. If the solutions are not real, state No Real Solution. $$ 2 x^{2}+5 x+3=0 $$

For each of the following exercises, find and plot the \(x\) -and \(y\) -intercepts, and graph the straight line based on those two points. $$4 x-3 y=12$$

For the following exercises, solve the equation by identifying the quadratic form. Use a substitute variable and find all real solutions by factoring. $$ \left(x^{2}-1\right)^{2}+\left(x^{2}-1\right)-12=0 $$

Graph both straight lines (left-hand side being \(y_{1}\) and right-hand side being \(y_{2}\) ) on the same axes. Find the point of intersection and solve the inequality by observing where it is true comparing the \(y\) -values of the lines. $$ x-2>2 x+1 $$

For the following exercises, graph the pair of equations on the same axes, and state whether they are parallel, perpendicular, or neither. \(x=4\) \(y=-3\)

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ i^{8} $$

Solve for \(h : A=\frac{1}{2} h\left(b_{1}+b_{2}\right)\)

Solve the quadratic equation by using the quadratic formula. If the solutions are not real, state No Real Solution. $$ x^{2}+x=4 $$

For each of the following exercises, find and plot the \(x\) -and \(y\) -intercepts, and graph the straight line based on those two points. $$x-2 y=8$$

\text { Solve for } h: A=\frac{1}{2} h\left(b_{1}+b_{2}\right)

For the following exercises, graph both straight lines (left-hand side being \(y_{1}\) and right-hand side being \(y_{2}\) ) on the same axes. Find the poin of intersection and solve the inequality by observing where it is true comparing the \(y\) -values of the lines. $$ x+1>x+4 $$

For the following exercises, solve the equation by identifying the quadratic form. Use a substitute variable and find all real solutions by factoring. $$ (x+1)^{2}-8(x+1)-9=0 $$

For the following exercises, find the slope of the line that passes through the given points. \((5,4)\) and \((7,9)\)

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ i^{15} $$

Solve the quadratic equation by using the quadratic formula. If the solutions are not real, state No Real Solution. $$ 2 x^{2}-8 x-5=0 $$

For each of the following exercises, find and plot the \(x\) -and \(y\) -intercepts, and graph the straight line based on those two points. $$y-5=5 x$$

For the following exercises, graph both straight lines (left-hand side being \(y_{1}\) and right-hand side being \(y_{2}\) ) on the same axes. Find the poin of intersection and solve the inequality by observing where it is true comparing the \(y\) -values of the lines. $$ \frac{1}{2} x+1>\frac{1}{2} x-5 $$

For the following exercises, solve the equation by identifying the quadratic form. Use a substitute variable and find all real solutions by factoring. $$ (x-3)^{2}-4=0 $$

For the following exercises, find the slope of the line that passes through the given points. \((-3,2)\) and \((4,-7)\)

Find the dimensions of an American football field. The length is \(200 \mathrm{ft}\) more than the width, and the perimeter is \(1,040 \mathrm{ft}\). Find the length and width. Use the perimeter formula \(P=2 L+2 W\).

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ i^{22} $$

Solve the quadratic equation by using the quadratic formula. If the solutions are not real, state No Real Solution. $$ 3 x^{2}-5 x+1=0 $$

For each of the following exercises, find and plot the \(x\) -and \(y\) -intercepts, and graph the straight line based on those two points. $$3 y=-2 x+6$$

Find the dimensions of an American football fi ld. The length is \(200 \mathrm{ft}\) ore than the width, and the perimeter is \(1,040 \mathrm{ft}\). Fi \(\mathrm{d}\) the length and width. Use the perimeter formula \(P=2 L+2 W\).

For the following exercises, graph both straight lines (left-hand side being \(y_{1}\) and right-hand side being \(y_{2}\) ) on the same axes. Find the poin of intersection and solve the inequality by observing where it is true comparing the \(y\) -values of the lines. $$ 4 x+1<\frac{1}{2} x+3 $$

For the following exercises, solve for the unknown variable. $$ x^{-2}-x^{-1}-12=0 $$

Graph both straight lines (left-hand side being \(y_{1}\) and right-hand side being \(y_{2}\) ) on the same axes. Find the point of intersection and solve the inequality by observing where it is true comparing the \(y\) -values of the lines. $$ 4 x+1<\frac{1}{2} x+3 $$

For the following exercises, find the slope of the line that passes through the given points. \((-5,4)\) and \((2,4)\)

Distance equals rate times time, \(d=r t\) . Find the distance Tom travels if he is moving at a rate of 55 \(\mathrm{mi} / \mathrm{h}\) for 3.5 \(\mathrm{h}\) .

For the following exercises, use a calculator to help answer the questions. Evaluate \((1+i)^{k}\) for \(k=4,8,\) and \(12 .\) Predict the value if \(k=16\).

Solve the quadratic equation by using the quadratic formula. If the solutions are not real, state No Real Solution. $$ x^{2}+4 x+2=0 $$

For each of the following exercises, find and plot the \(x\) -and \(y\) -intercepts, and graph the straight line based on those two points. $$y=\frac{x-3}{2}$$

For the following exercises, write the set in interval notation. $$ \\{x |-1< x <3\\} $$

For the following exercises, solve for the unknown variable. $$ \sqrt{|x|^{2}}=x $$

Write the set in interval notation. $$ \\{x \mid-1

For the following exercises, find the slope of the line that passes through the given points. \((-1,-2)\) and \((3,4)\)

For the following exercises, use a calculator to help answer the questions. Evaluate \((1-i)^{k}\) for \(k=2,6,\) and \(10 .\) Predict the value if \(k=14 .\)

Solve the quadratic equation by using the quadratic formula. If the solutions are not real, state No Real Solution. $$ 4+\frac{1}{x}-\frac{1}{x^{2}}=0 $$

For the following exercises, write the set in interval notation. $$ \\{x | x \geq 7\\} $$

For the following exercises, solve for the unknown variable. $$ t^{10}-t^{5}+1=0 $$

Write the set in interval notation. $$ \\{x \mid x \geq 7\\} $$

For the following exercises, find the slope of the line that passes through the given points. \((3,-2)\) and \((3,-2)\)